Probabilistic Tractography
J. Donald Tournier1
1Department of Biomedical Engineering, School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom

Synopsis

Probabilistic tractography approaches account for the inherent, multiple sources of uncertainty that impact on the fibre tracking process. They aim to provide a more representative depiction of the range of connections that are consistent with the data. These approaches typically depend on the availability of the distribution of fibre orientations, from which statistical samples can be obtained and used in the streamline propagation process. It is important to note that probabilistic approaches do not in general provide estimates of the probability of a connection; they aim to depict the full range of likely connections that are consistent with the data.

Why probabilistic tractography?

Tractography operates by 'tracking' the estimated orientation of the white matter fibres through the brain. Any errors in these fibre orientation estimates will therefore propagate into errors in the streamlines produced [1,2]. Furthermore, the longer the streamline is allowed to propagate, the more these errors will accumulate. Deterministic tractography methods only provide the single 'best' estimate of the pathway being reconstructed from a given seed point, with no indication of the likely impact of errors in the estimation.
Unfortunately, there are many sources of uncertainty in fibre orientation estimation, and the tractography process in general:
  1. The contrast in diffusion MRI (dMRI) is based on strong attenuation of the signal, leading to images with low signal to noise ratio (SNR); in fact, the signal is often within the noise floor, particularly when using high b-values. This translates into noise in the estimated fibre orientations.
  2. Modern fibre orientation estimation techniques provide multiple fibre orientations. When several candidate directions are available, the streamline propagation algorithm has to make a decision as to which direction to follow. In many cases, there is no obvious 'right' answer, which introduces uncertainty in the results.
  3. White matter fibres can be arranged in different configurations within a single voxel (crossing, curving, fanning, ...), many of which lead to the same dMRI signal. One such ambiguity is the well-known crossing vs, 'kissing' problem. Where there is ambiguity as to how the fibres are arranged, there is uncertainty in how to propagate streamlines through this voxel.
  4. The dMRI signal is inherently smooth as a function of orientation, placing a practical limit on the angular resolution of the estimated fibre orientation density function (fODF).
  5. White matter axons do not travel in perfectly straight lines, and will naturally 'wiggle' around within their parent fascicle. This introduces dispersion in the fODF, placing an intrinsic limit on its angular resolution.
Given all these sources of uncertainty, and the expected complexity of the organisation of the white matter in the brain, it is important to use methods that can provide a realistic estimate of the full range of possible paths that are consistent with the data, motivating the use of probabilistic approaches to tractography.

How is probabilistic tractography done?

Many approaches have been proposed to perform some form of probabilistic tractography, with many relying on the probabilistic streamlines paradigm. Briefly, these methods operate in the same way as deterministic streamlines, with one simple modification: at each step, the orientation to follow is taken as a sample (in the statistical sense) from the distribution of fibre orientations. Different streamlines generated from the same seed point will therefore not follow exactly the same path (as they would with deterministic approaches), but will explore the range of likely paths that remain in some sense consistent with the data, given its inherent level of uncertainty. With probabilistic approaches, it is common practice to generate many more streamlines than would be deemed sufficient for deterministic approaches, providing a broader representation of the range of likely connections, rather than the single best estimate as provided with deterministic tractography.
The derivation of the distribution of fibre orientation is therefore a fundamental aspect of probabilistic tractography. A variety of methods have been proposed to do this, ranging from heuristic approaches [3], statistical resampling approaches (aka bootstrapping) [4,5], and Bayesian inference methods [6,7] to using the fibre ODF directly [8]. These implicitly account for different sources of uncertainty, and make different assumptions regarding the range of expected fibre configurations.

Interpretation of probabilistic results

It is tempting to assume that probabilistic tractography can provide an estimate of the probability of connection for a given pathway. This is unfortunately not the case: there are many confounding factors that affect the results, ranging from seed region size & placement, distance to target region, and the presence of branching or 'fanning' in the pathways delineated, amongst others.
A more accurate way to interpret the data is to view the set of streamlines generated as a representative sample from the distribution of paths that are consistent with the data (given the limitations of the specific methods used). While a range of methods have been proposed to attempt to derive more reliable indices of 'probability' for individual connections, such interpretations are nonetheless problematic and probably best avoided.

Acknowledgements

This work received funding from the European ResearchCouncil under the European Union’s Seventh Framework Pro-gramme ([FP7/2007-2013/ERC] grant agreement no. [319456]dHCP project), and was supported by the Wellcome/EPSRCCentre for Medical Engineering at King’s College Lon-don [WT 203148/Z/16/Z]; the Medical Research Council[MR/K006355/1] and by the National Institute for Health Re-search (NIHR) Biomedical Research Centre based at Guy’s andSt Thomas’ NHS Foundation Trust and King’s College London.The views expressed are those of the author(s) and not neces-sarily those of the NHS, the NIHR or the Department of Health.

References

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Proc. Intl. Soc. Mag. Reson. Med. 29 (2021)